{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:J75BDQCNT7RJTO2OM4L3I4I5BF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"722cffd547e1e26abe07464e4d79e6cd2cb892c969b163642ea380d0d69af978","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-12-02T20:22:28Z","title_canon_sha256":"b75727c25898dd54c2f7c2bb4080c7105b32103532f69fae77c40eae7b22f0c3"},"schema_version":"1.0","source":{"id":"1812.00459","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00459","created_at":"2026-05-17T23:59:21Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00459v1","created_at":"2026-05-17T23:59:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00459","created_at":"2026-05-17T23:59:21Z"},{"alias_kind":"pith_short_12","alias_value":"J75BDQCNT7RJ","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"J75BDQCNT7RJTO2O","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"J75BDQCN","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:fbeec96816dc565b779aac48419a187bbf02044581ffa0bcd7a65e28c68a9878","target":"graph","created_at":"2026-05-17T23:59:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at odd positive integers.","authors_text":"Fritz Gesztesy, Hagop Tossounian, Klaus Kirsten, Lance Littlejohn, Lotfi Hermi, Mark S. Ashbaugh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-12-02T20:22:28Z","title":"Trace formulas applied to the Riemann $\\zeta$-function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00459","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d21f648e42a43531952dc4dcd38589eb0ff77bbf891c08f5e6d411a141e192ca","target":"record","created_at":"2026-05-17T23:59:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"722cffd547e1e26abe07464e4d79e6cd2cb892c969b163642ea380d0d69af978","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-12-02T20:22:28Z","title_canon_sha256":"b75727c25898dd54c2f7c2bb4080c7105b32103532f69fae77c40eae7b22f0c3"},"schema_version":"1.0","source":{"id":"1812.00459","kind":"arxiv","version":1}},"canonical_sha256":"4ffa11c04d9fe299bb4e6717b4711d094e96b8beb13cea9d6f50fb3d70e179c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ffa11c04d9fe299bb4e6717b4711d094e96b8beb13cea9d6f50fb3d70e179c3","first_computed_at":"2026-05-17T23:59:21.288307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:21.288307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9M1rrNlBerXJe31a39v22FqCU8RQ+8BIErElOChZxlawcn7xS1miiHilfwYrX94RdovP1i6MKms8k3WW4wB6DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:21.288910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00459","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d21f648e42a43531952dc4dcd38589eb0ff77bbf891c08f5e6d411a141e192ca","sha256:fbeec96816dc565b779aac48419a187bbf02044581ffa0bcd7a65e28c68a9878"],"state_sha256":"e946f0f0b388227a252b16efb45f1635b2f3ddf29276013963e91285198c4398"}